#=====================================================================
#= get external packages
import numpy as np
import matplotlib.pyplot as plt
from mpl_toolkits.mplot3d import Axes3D

#=====================================================================

Gw1 = plt.figure("Sphere-Cylinder Intersection")
diagram1 = Axes3D(Gw1)
diagram1.view_init(33,-48)

#= force equal aspect ratio in all 3 directions
#= 3D library is missing this -- force it with an invisible bounding cube
diagram1.set_aspect('equal')
CUBE = 1.3
for direction in (-1, 1):
    for point in np.diag(direction * CUBE * np.array([1,1,1])):
        diagram1.plot([point[0]], [point[1]], [point[2]], 'white')

#= line for y-axis (show as N/E/D coords, not plotting coords)
diagram1.plot([0.0,1.5],[0.0,0.0],[0.0,0.0],
              linewidth=1,linestyle='-',color='black')
diagram1.text(1.6,0.0,0.0,'y',fontsize=14,fontweight='bold')

#= line for x-axis (show as N/E/D coords, not plotting coords)
diagram1.plot([0.0,0.0],[0.0,1.5],[0.0,0.0],
              linewidth=1,linestyle='-',color='black')
diagram1.text(0.0,1.6,0.0,'x',fontsize=14,fontweight='bold')

#= line for z-axis (show as N/E/D coords, not plotting coords)
diagram1.plot([0.0,0.0],[0.0,0.0],[0.0,-1.5],
              linewidth=1,linestyle='-',color='black')
diagram1.text(0.0,0.0,-1.7,'z',fontsize=14,fontweight='bold')

#= unit sphere about origin
phi = np.linspace(0.0,np.pi/2.0,361)
theta = np.linspace(0.0,np.pi,361)
phi,theta = np.meshgrid(phi,theta)
x = np.sin(theta)*np.cos(phi)
y = np.sin(theta)*np.sin(phi)
z = np.cos(theta)
diagram1.plot_surface(x,y,z,linewidth=0.0,color='DarkKhaki',alpha=0.25)

#= elliptical cylinder about z-axis 1
a = 0.10
b = 0.15
x = a*np.cos(np.linspace(0.0,np.pi/2.0,101))
z = np.linspace(-1.3,1.3,101)
x,z = np.meshgrid(x,z)
y = b*np.sin(np.arccos(x/a))
diagram1.plot_surface(x,y,z,linewidth=0.0,color='red',alpha=0.25)

#= elliptical cylinder about z-axis 2
a = 0.21
b = 0.315
x = a*np.cos(np.linspace(0.0,np.pi/2.0,101))
z = np.linspace(-1.3,1.3,101)
x,z = np.meshgrid(x,z)
y = b*np.sin(np.arccos(x/a))
diagram1.plot_surface(x,y,z,linewidth=0.0,color='red',alpha=0.25)

#= elliptical cylinder about z-axis 3
a = 0.42
b = 0.63
x = a*np.cos(np.linspace(0.0,np.pi/2.0,101))
z = np.linspace(-1.3,1.3,101)
x,z = np.meshgrid(x,z)
y = b*np.sin(np.arccos(x/a))
diagram1.plot_surface(x,y,z,linewidth=0.0,color='red',alpha=0.25)

#= sphere-cylinder intersection 1
a = 0.10
b = 0.15
x = a*np.cos(np.linspace(0.0,np.pi/2.0,101))
y = b*np.sin(np.linspace(0.0,np.pi/2.0,101))
z = np.sqrt(np.around(1.0-x**2-y**2,decimals=10))
diagram1.plot(x,y,z,linewidth=1.0,linestyle='-',color='red')
diagram1.plot(x,y,-z,linewidth=1.0,linestyle='-',color='red')

#= sphere-cylinder intersection 2
a = 0.21
b = 0.315
x = a*np.cos(np.linspace(0.0,np.pi/2.0,101))
y = b*np.sin(np.linspace(0.0,np.pi/2.0,101))
z = np.sqrt(np.around(1.0-x**2-y**2,decimals=10))
diagram1.plot(x,y,z,linewidth=1.0,linestyle='-',color='red')
diagram1.plot(x,y,-z,linewidth=1.0,linestyle='-',color='red')

#= sphere-cylinder intersection 3
a = 0.42
b = 0.63
x = a*np.cos(np.linspace(0.0,np.pi/2.0,101))
y = b*np.sin(np.linspace(0.0,np.pi/2.0,101))
z = np.sqrt(np.around(1.0-x**2-y**2,decimals=10))
diagram1.plot(x,y,z,linewidth=1.0,linestyle='-',color='red')
diagram1.plot(x,y,-z,linewidth=1.0,linestyle='-',color='red')

#= plotting axes off
diagram1.axis('off')

#= display/save
plt.savefig ("Diagram_Axes_1_raw.pdf")
plt.savefig ("Diagram_Axes_1_raw.svg")
plt.savefig ("Diagram_Axes_1_raw.png")
plt.show()